When asked if the majority leader's defeat makes it harder to move forward on immigration reform, Boehner said, "We don't know that that [immigration] is the issue -- or was the issue -- in the election."

Cantor's lukewarm support for some sort of immigration reform -- even though the issue was going nowhere -- was one of many issues that his conservative challenger, economics professor David Brat, used to paint Cantor as an establishment sellout who's out of touch with the right.

Boehner also declined to endorse anyone in the GOP conference election on June 19 to succeed Cantor as majority leader. "Members are going to make this decision," he said, and "I can work with whoever gets elected." House Majority Whip Kevin McCarthy (R-CA) is the favorite to ascend to the position.